The universal Glivenko-Cantelli property

Let F be a separable uniformly bounded family of measurable functions on a standard measurable space, and let N_{[]}(F,\epsilon,\mu) be the smallest number of \epsilon-brackets in L^1(\mu) needed to cover F. The following are equivalent: 1. F is a universal Glivenko-Cantelli class. 2. N_{[]}(F,\epsilon,\mu)0 and every probability measure \mu. 3. F is totally bounded in L^1(\mu) for every probability measure \mu. 4. F does not contain a Boolean \sigma-independent sequence. It follows that universal Glivenko-Cantelli classes are uniformity classes for general sequences of almost surely convergent random measures.Comment: 26 page

MammoWave Breast Imaging Device: Prospective Clinical Trial Results and AI Enhancement

Penalised PET image reconstruction algorithms are often accelerated during early iterations with the use of subsets. However, these methods may exhibit limit cycle behaviour at later iterations due to variations between subsets. Desirable converged images can be achieved for a subclass of these algorithms via the implementation of a relaxed step size sequence, but the heuristic selection of parameters will impact the quality of the image sequence and algorithm convergence rates. In this work, we demonstrate the adaption and application of a class of stochastic variance reduction gradient algorithms for PET image reconstruction using the relative difference penalty and numerically compare convergence performance to BSREM. The two investigated algorithms are: SAGA and SVRG. These algorithms require the retention in memory of recently computed subset gradients, which are utilised in subsequent updates. We present several numerical studies based on Monte Carlo simulated data and a patient data set for fully 3D PET acquisitions. The impact of the number of subsets, different preconditioners and step size methods on the convergence of regions of interest values within the reconstructed images is explored. We observe that when using constant preconditioning, SAGA and SVRG demonstrate reduced variations in voxel values between subsequent updates and are less reliant on step size hyper-parameter selection than BSREM reconstructions. Furthermore, SAGA and SVRG can converge significantly faster to the penalised maximum likelihood solution than BSREM, particularly in low count data

Guidelines for the Selection of Physical Literacy Measures in Physical Education in Australia

Assessment of physical literacy poses a dilemma of what instrument to use. There is currently no guide regarding the suitability of common assessment approaches. The purpose of this brief communication is to provide a user's guide for selecting physical literacy assessment instruments appropriate for use in school physical education and sport settings. While recommendations regarding specific instruments are not provided, the guide offers information about key attributes and considerations for the use. A decision flow chart has been developed to assist teachers and affiliated school practitioners to select appropriate methods of assessing physical literacy. School PE and sport scenarios are presented to illustrate this process. It is important that practitioners are empowered to select the most appropriate instrument/s to suit their needs

Defining Physical Literacy for Application in Australia: A Modified Delphi Method

Purpose. The development of a physical literacy definition and standards framework suitable for implementation in Australia. Method. Modified Delphi methodology. Results . Consensus was established on four defining statements: Core – Physical literacy is lifelong holistic learning acquired and applied in movement and physical activity contexts; Composition – Physical literacy reflects ongoing changes integrating physical, psychological, cognitive and social capabilities; Importance – Physical literacy is vital in helping us lead healthy and fulfilling lives through movement and physical activity; Aspiration – A physically literate person is able to draw on their integrated physical, psychological, cognitive, and social capacities to support health promoting and fulfilling movement and physical activity, relative to their situation and context, throughout the lifespan. The standards framework addressed four learning domains (physical, psychological, cognitive, and social), spanning five learning configurations/levels. Conclusion. The development of a bespoke program for a new context has important implications for both existing and future program

Fire Ant Alate Wing Motion Data and Numerical Reconstruction

The wing motions of a male and a female fire ant alate, which beat their wings at 108 and 96 Hz, respectively, were captured with a stereo imaging system at a high frame rate of 8,000 frames per second. By processing the high-speed image frames, the three-dimensional wingtip positions and the wing surface orientation angles were determined with a high phase resolution, i.e. 74 and 83 phases per period for the male and the female, respectively. A numerical reconstruction of the stereo wingbeat images demonstrated that the data collected described almost all the details of the wing surface motion, so that further computational fluid dynamic simulations are possible for fire ant alate flight

Growth Based Morphogenesis of Vertebrate Limb Bud

Many genes and their regulatory relationships are involved in developmental phenomena. However, by chemical information alone, we cannot fully understand changing organ morphologies through tissue growth because deformation and growth of the organ are essentially mechanical processes. Here, we develop a mathematical model to describe the change of organ morphologies through cell proliferation. Our basic idea is that the proper specification of localized volume source (e.g., cell proliferation) is able to guide organ morphogenesis, and that the specification is given by chemical gradients. We call this idea “growth-based morphogenesis.” We find that this morphogenetic mechanism works if the tissue is elastic for small deformation and plastic for large deformation. To illustrate our concept, we study the development of vertebrate limb buds, in which a limb bud protrudes from a flat lateral plate and extends distally in a self-organized manner. We show how the proportion of limb bud shape depends on different parameters and also show the conditions needed for normal morphogenesis, which can explain abnormal morphology of some mutants. We believe that the ideas shown in the present paper are useful for the morphogenesis of other organs